How to make a perfectly flat bottom for 3D-printing topographic relief?
The solidify modifier can be removed, if you need to do this kind of thing a few times do this instead:


Select your Mesh, go to Edit Mode, Select All geometry.
Hit E to Extrude, Then Z followed by Z again to constrain the direction
Then move the mouse to the right, and the newly extruded geometry will start to move down. You can see by exactly how much in the bottom left (by default the contrast between the text and the panel make this unnecessarily hard to read (April 2015). But it looks like this




You can use the mouse, or left / right keys, or even type the number you want directly with the num keys.


then to flatten the new geometry, hit S, Z, follwed by number 0. 


Here's a view from the underneath before and after the flatten.



Cons:

there are all kinds of factors that can interfere with how straightford this is, the location of the reliefs Object origin being one of them. If I had to do this repeatedly, it would be something to write a small python script for.

The recipe for such a script might be:


find lowest z coordinate of the original mesh
extrude all faces a little bit
replace all z values of the newly geometry with the lowest z of the original mesh minus the desired thickness.


This would produce a mesh with a minimum thickness.